By Aurora Marica,Enrique Zuazua

This work describes the propagation houses of the so-called symmetric inside penalty discontinuous Galerkin (SIPG) approximations of the 1-d wave equation. this can be performed through linear approximations on uniform meshes. First, a cautious Fourier research is developed, highlighting the coexistence of 2 Fourier spectral branches or spectral diagrams (physical and spurious) on the topic of the 2 parts of the numerical answer (averages and jumps). effective filtering mechanisms also are developed by technique of concepts formerly proved to be acceptable for classical schemes like finite adjustments or P1-classical finite parts. In particular, the paintings provides an explanation that the uniform observability estate is recovered uniformly through contemplating preliminary info with null jumps and averages given via a bi-grid filtering set of rules. eventually, the book explains how these results could be prolonged to different extra subtle conforming and non-conforming finite aspect tools, specifically to quadratic finite elements, neighborhood discontinuous Galerkin equipment and a model of the SIPG procedure including penalization at the common derivatives of the numerical resolution on the grid points.  This paintings is the 1st ebook to contain a rigorous research of the discontinuous Galerkin equipment for wave regulate difficulties. will probably be of curiosity to more than a few researchers specializing in wave approximations.

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